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Book Reviews

Review of Ars Magna or the Rules of Algebra

Reviewed by a reader, from Tuebingen, Germany
The "Ars Magna" by Girolamo Cardano is one of the most important books of the 16th century, a milestone for algebra and mathematics. With its new way of treating scientific problems, it's also a typical representant of the Italian Renaissance. This is a long overdue re-issue, translated from Latin into English and adapted to modern mathematical syntax. Mathematicians and historians both will enjoy it!

Review of Algebra 1, 1983

Reviewed by Michael K. Drotar, from Portland, Oregon United States
This is by far one of the best math books in the Dover catalogue. While the prose is admittedly dry, the clarity of the exposition is flawless. The author begins his discussion with a chapter on set theory and wisely takes an intuitive appraoch rather than a theoretical one. This makes the second chapter, which gives an axiomatic account of the fundamentals of Boolean algebra, much easier to digest. Once you master the first two chapters, the rest of the books is smooth sailing. From here the author gives detailed, yet succinct, accounts of the applicatons of Boolean algebra to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. Although the book is aimed primarily at math, computer science, and electrical engineering majors, it accessible to anyone who is comfortable with college level mathematics. It is especially helpful to the philosophy student who wishes to learn about symbolic logic and its applications to the foundations of computer science.

Reviewed by Mac, from Los Angeles area
Though written with dry prose, this book is very much worth studying to anyone with an interest in the subject.Targeted toward math and computer science undergraduates and to a certain extent electrical engineering types, the book progresses like a math course. It gives the greatest emphasis to the key topics (like the title) and builds on the most basic sub-topics. In Boolean Algebra, that sub-topic is Set Theory. Therefore this book requires a level of thinking beyond the ordinary, but once you understand Set Theory, the rest is easy. And to make it easier on the reader, the lessons on Set Theory are totally intuitive, assuming the reader has at least taken algebra.

Reviewed by newton fisher, from riverside, ca
This book fell to the floor where it was pounced upon and chewed by my nieces 3 pound dog who 'forthwith' lost 10 pounds of the nectar of life. We shall be suing Dover for her wrongful death by dehydration. Boolean Algebra is a fine subject but this book ... the most turgid bit of writing since 'OG the trog-dude' first scratched a mark on a cave wall.

Review of Introductory Algebra for College Students and Math Skills for College Students and How to Study Math Package

Editorial review
The purpose of this book is to give a thorough introduction to the most commonly used methods of numerical linear algebra and optimisation. The prerequisites are some familiarity with the basic properties of matrices, finite-dimensional vector spaces, advanced calculus, and some elementary notations from functional analysis. The book is in two parts. The first deals with numerical linear algebra (review of matrix theory, direct and iterative methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimisation (general algorithms, linear and nonlinear programming). The author has based the book on courses taught for advanced undergraduate and beginning graduate students and the result is a well-organised and lucid exposition. Summaries of basic mathematics are provided, proofs of theorems are complete yet kept as simple as possible, and applications from physics and mechanics are discussed. Professor Ciarlet has also helpfully provided over 40 line diagrams, a great many applications, and a useful guide to further reading. This excellent textbook, which is translated and revised from the very successful French edition, will be of great value to students of numerical analysis, applied mathematics and engineering.

Review of Algebra and Practical Applications

Editorial review
Happel presents an introduction to the use of triangulated categories in the study of representations of finit-dimensional algeras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite=dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and iterated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. With a comprehensive reference section, algebraists and research students in this field will find this an indispensable account of the theory of finite-dimensional algebras.

Review of Prealgebra

Editorial review
Modern computer networks now circle the world, but the transmission of information between them depends on the many different protocols that define the behaviour of the sender and receiver. It is clear therefore, that the accurate description of these protocols is important if harmonious communication is to be maintained. In this book the authors use the formal specification language PSF to provide an unambiguous description of several communication protocols of varying levels of complexity, ranging from the alternating bit protocol to the token ring protocol. Beginners, as well as professionals in the field of communication protocols, will benefit from both the methods of specification described and the protocols discussed in this book.

Review of Multiplicities and Chern Classes in Local Algebra

Editorial review
The theory of local Chern characters used in commutative algebra originated in topology about thirty years ago, and from there was introduced in algebraic geometry. This book describes the theory in an algebraic setting, presenting recent research results and important algebraic applications, some of which come from the author's own work. It concentrates on the background in commutative algebra and homological algebra and describes the relations between these subjects, including extensive discussions of the homological conjectures and of the use of the Frobenius map. It will be particularly useful for graduate students and researchers.

Review of Casio 9850 Graphic Module to Accompany College Algebra, Graphs and Models and Algebra and Trigonomet

Editorial review
Finite fields are algebraic structures in which there is much research interest. This book gives a state-of-the-art account of finite fields and their applications in communications (coding theory, cryptology), combinatorics, design theory, quasirandom points, algorithms and their complexity. Typically, theory and application are tightly interwoven in the survey articles and original research papers included here. The book also demonstrates interconnections with other branches of pure mathematics such as number theory, group theory and algebraic geometry. This volume is an invaluable resource for any researcher in finite fields or related areas.

Review of More Practising Algebra

Editorial review
Practising Algebra is aimed at the students in the senior years of secondary education and covers work which spans Years 11and 12, with some more advanced material, depending upon course content and state. The material can serve as: - as support for day to day work - as revision for tests - as a reference for other set work Each section follows the same format: - a summary of the skills involved in the section - a number of single focus skills exercises - a true/false exercise to alert students to important facts - an exercise of applications of the skills in the section Each single focus exercise is preceeded by a worked example, the 'boxed' presentation makes it easy to identify and follow.

Review of Intermediate Algebra, Revised Prelim

Editorial review
This workbook/CD-ROM package is almost identical to the package published in mid-2001 under ISBN 0-534-39009-9, except for the addition of an updated introductory pamphlet, to be used instead of pages ix to xxxiv in the bound book. Designed for a computer-based course, the workbook contains exercises on real numbers, exponents, the language of algebra, linear equations, relations and functions, equations and inequalities, roots and radicals, polynomials, quadratic equations, ratios and rates, and rational expressions. Selected answers are included. The three CD-ROMs run on all Windows and Macinstosh platforms, on stand-alone computers, over a LAN, and over the internet.Book News, Inc.®, Portland, OR


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